Details

sample48.0ms

Algorithm

intervals

Results

24.0ms	255×	body	80	valid
0.0ms	1×	body	320	valid

simplify131.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	33	10
1	79	10
2	210	10
3	483	10
4	910	10
5	1516	10
6	2818	10
7	5001	10

prune5.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 23.9b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
1.5b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
1.8b	(+ (* (+ x y) z) (* (+ t y) a))
22.4b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

1050×	`*-un-lft-identity`
500×	`distribute-lft-out`
450×	`associate-l`
153×	`add-sqr-sqrt`
144×	`prod-diff`
140×	`distribute-lft-out--`
125×	`times-frac`
90×	`add-cube-cbrt`
42×	`associate-r`
25×	`associate-/l*`
21×	`unswap-sqr`
14×	`*-commutative` `difference-of-squares`
13×	`fma-def`
12×	`fma-neg`
11×	`add-log-exp`
10×	`associate-*l/`
8×	`add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `flip-+`
6×	`pow1`
5×	`associate-/r*`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u`
2×	`+-commutative` `flip3--` `diff-log` `associate--l+` `sum-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `cbrt-unprod` `div-inv`

Counts

4 → 431

Calls

4 calls:

6.0ms	(* (+ x y) z)
38.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
19.0ms	(+ (* (+ x y) z) (* (+ t y) a))
55.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series867.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (+ x y) z)
109.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
58.0ms	(+ (* (+ x y) z) (* (+ t y) a))
671.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify172.0ms

Algorithm

egg-herbie

Counts

443 → 443

Iterations

Useful iterations: 2 (120.0ms)

Iter	Nodes	Cost
0	784	6001
1	3379	4672
2	5001	4666

prune405.0ms

Filtered

443 candidates to 117 candidates (26.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	435	8	443
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	436	8	444

Merged error: 7.1b

Counts

444 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.5b	(fma (+ x y) z (* (+ t y) a))
7.9b	(/ (* y b) (+ (+ x t) y))
20.7b	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

232×	`*-un-lft-identity`
179×	`times-frac`
109×	`add-sqr-sqrt`
95×	`add-cube-cbrt`
82×	`distribute-lft-out`
28×	`associate-/l*`
22×	`associate-l`
21×	`associate-r`
18×	`add-exp-log`
16×	`add-cbrt-cube`
13×	`associate-/r*`
9×	`associate-/l/`
8×	`div-inv`
7×	`div-exp` `*-commutative` `unswap-sqr`
6×	`pow1`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
2×	`associate-*l/` `prod-exp` `cbrt-unprod`
1×	`1-exp` `pow-prod-down` `fma-udef`

Counts

4 → 239

Calls

4 calls:

6.0ms	(* (+ t y) a)
1.0ms	(fma (+ x y) z (* (+ t y) a))
11.0ms	(/ (* y b) (+ (+ x t) y))
12.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

series401.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (+ t y) a)
57.0ms	(fma (+ x y) z (* (+ t y) a))
83.0ms	(/ (* y b) (+ (+ x t) y))
239.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

simplify119.0ms

Algorithm

egg-herbie

Counts

251 → 251

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	749	2431
1	3466	2256
2	5001	2153

prune438.0ms

Filtered

251 candidates to 135 candidates (53.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	248	3	251
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	252	7	259

Merged error: 4.7b

Counts

259 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ y (+ (+ x t) y))
1.5b	(fma (+ x y) z (* (+ t y) a))
4.3b	(* b (/ y (+ (+ x t) y)))
20.7b	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

195×	`*-un-lft-identity`
150×	`times-frac`
89×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
66×	`distribute-lft-out`
23×	`associate-/l*`
21×	`associate-r`
18×	`add-exp-log` `associate-/r*`
16×	`add-cbrt-cube`
11×	`associate-*r/`
9×	`div-inv` `associate-/l/`
7×	`div-exp`
6×	`pow1` `associate-/r/`
5×	`cbrt-undiv` `clear-num`
4×	`expm1-log1p-u` `frac-2neg` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `associate-l` `flip-+`
2×	`prod-exp` `un-div-inv` `cbrt-unprod` `unswap-sqr`
1×	`1-exp` `pow-prod-down` `*-commutative` `fma-udef`

Counts

4 → 214

Calls

4 calls:

7.0ms	(/ y (+ (+ x t) y))
1.0ms	(fma (+ x y) z (* (+ t y) a))
13.0ms	(* b (/ y (+ (+ x t) y)))
11.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

series406.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ y (+ (+ x t) y))
56.0ms	(fma (+ x y) z (* (+ t y) a))
52.0ms	(* b (/ y (+ (+ x t) y)))
236.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

simplify93.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	603	2115
1	2641	1937
2	5003	1834

prune383.0ms

Filtered

226 candidates to 120 candidates (53.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	225	1	226
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	227	6	233

Merged error: 2.4b

Counts

233 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ x t) y))
1.5b	(fma (+ x y) z (* (+ t y) a))
7.9b	(/ (* y b) (+ (+ x t) y))
20.7b	(* (fma (+ x y) z (* (+ t y) a)) (/ 1 (+ (+ x t) y)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

164×	`*-un-lft-identity`
92×	`times-frac`
76×	`add-sqr-sqrt`
63×	`distribute-lft-out`
57×	`add-cube-cbrt`
39×	`associate-r`
22×	`add-exp-log`
21×	`associate-l`
19×	`associate-/l*`
16×	`add-cbrt-cube`
15×	`associate-/r*`
11×	`associate-*r/`
9×	`unswap-sqr`
7×	`pow1` `*-commutative`
6×	`div-exp` `associate-/r/`
5×	`prod-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `clear-num` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `flip3-+` `un-div-inv` `cbrt-unprod` `flip-+` `div-inv`
2×	`rec-exp` `1-exp`
1×	`pow-flip` `pow-prod-down` `fma-udef` `inv-pow`

Counts

4 → 206

Calls

4 calls:

13.0ms	(/ 1 (+ (+ x t) y))
1.0ms	(fma (+ x y) z (* (+ t y) a))
10.0ms	(/ (* y b) (+ (+ x t) y))
14.0ms	(* (fma (+ x y) z (* (+ t y) a)) (/ 1 (+ (+ x t) y)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ 1 (+ (+ x t) y))
49.0ms	(fma (+ x y) z (* (+ t y) a))
79.0ms	(/ (* y b) (+ (+ x t) y))
239.0ms	(* (fma (+ x y) z (* (+ t y) a)) (/ 1 (+ (+ x t) y)))

simplify86.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	525	1537
1	2457	1406
2	5003	1360

prune391.0ms

Filtered

218 candidates to 125 candidates (57.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	218	6	224

Merged error: 2.4b

Counts

224 → 6

regimes363.0ms

Accuracy

28.4% (16.3b remaining)

Error of 19.5b against oracle of 3.2b and baseline of 25.9b

bsearch121.0ms

Steps

Iters	Range		Point
8	4.3655482825599396e+57	4.8632694329972866e+61	3.7107450165740636e+61
10	-2.1855943307498512e+100	-2.086836314435331e+89	-1.9288964540011012e+93

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	18
1	40	18

end0.0ms

sample631.0ms

Algorithm

intervals

Results

365.0ms	7996×	body	80	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	320	valid